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2. System of linear equations - Wikipedia

   en.wikipedia.org/wiki/System_of_linear_equations

   A solution of a linear system is an assignment of values to the variables ,, …, such that each of the equations is satisfied. The set of all possible solutions is called the solution set. [5] A linear system may behave in any one of three possible ways: The system has infinitely many solutions.

3. Linear combination - Wikipedia

   en.wikipedia.org/wiki/Linear_combination

   This system of linear equations can easily be solved. First, the first equation simply says that a 3 is 1. Knowing that, we can solve the second equation for a 2, which comes out to −1. Finally, the last equation tells us that a 1 is also −1. Therefore, the only possible way to get a linear combination is with these coefficients. Indeed,

4. Consistent and inconsistent equations - Wikipedia

   en.wikipedia.org/wiki/Consistent_and...

   The system + =, + = has exactly one solution: x = 1, y = 2 The nonlinear system + =, + = has the two solutions (x, y) = (1, 0) and (x, y) = (0, 1), while + + =, + + =, + + = has an infinite number of solutions because the third equation is the first equation plus twice the second one and hence contains no independent information; thus any value of z can be chosen and values of x and y can be ...

5. Turing machine equivalents - Wikipedia

   en.wikipedia.org/wiki/Turing_machine_equivalents

   This is the same as an ordinary k-string Turing machine, except that the transition function δ is restricted so that the input tape can never be changed, and so that the output head can never move left. This model allows us to define deterministic space classes smaller than linear.

6. Linear system - Wikipedia

   en.wikipedia.org/wiki/Linear_system

   In other words, if the input x(t) to a linear system is = where δ(t) represents the Dirac delta function, and the corresponding response y(t) of the system is (=) = (,) then the function h(t 2, t 1) is the time-varying impulse response of the system.

7. Underdetermined system - Wikipedia

   en.wikipedia.org/wiki/Underdetermined_system

   It is inconsistent if and only if 0 = 1 is a linear combination (with polynomial coefficients) of the equations (this is Hilbert's Nullstellensatz). If an underdetermined system of t equations in n variables (t < n) has solutions, then the set of all complex solutions is an algebraic set of dimension at least n - t.